The entire notion of "smart" and "dumb" as singular states of intelligence is, well, dumb. People have different strengths and weaknesses in the way their brains work. For instance AJ Green scored incredibly badly on his Wonderlic recently, which makes him "dumb" in one sense, but his spatial intelligence is probably great and his kinesthetic intelligence (which covers things like hand/eye coordination and muscle memory) off the charts.
As for Palin, she's clearly very smart when it comes to interpersonal intelligence - reading people and relating to them. In the areas which are generally accepted as 'real intelligence' though - linguistic, mathematic, even philosophical/existential - she seems to be badly lacking. That profile matches up pretty well with what I know of Quayle too, and in both cases that goes beyond 10 second soundbites.
It doesn't match up with Adm. Stockdale though. His linguistic intelligence -- at least by the time in his life when he was Perot's VP candidate -- was pitiful, but as an extremely well-respected and decorated officer he likely would have has something close to genius level spatial intelligence, with his mathematic and kinesthetic intelligence not too far behind.
Is Palin "dumb"? In a lot of ways, incredibly so. On the other hand, she's pulling in more money than anybody in this thread, so by that measure she's smarter than any of us.